### Question 7.The mean price of a new car sold in Brooklyn is $ \mu = \$22,500 $. The standard deviation is $ \sigma = \$4,000 $. A sample of 100 new cars is chosen. Find the probability that:a. The sample mean $ \bar{X} > \$23,000 $b. The sampling error is less than \$800.### Explanation:This question involves understanding statistical concepts like mean, standard deviation, sample size, and the Central Limit Theorem.To solve part (a), one would need to compute the Z-score for the sample mean and then use the standard normal distribution to find the corresponding probability.For part (b), the concept of sampling error and its relation to the standard error of the mean would be demonstrated. The standard error (SE) can be calculated using the formula:\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \]where- $ \sigma $ is the standard deviation,- $ n $ is the sample size.The standard error will be used to find the probability that the sample mean falls within a certain range of the population mean (given the sampling error).

According to the Central Limit Theorem, the sampling distribution of sample means follow normal…

7. The mean price of a new car sold in Brooklyn is u =$22,500. o = $4,000. A sample of 100 new cars is chosen.. Find the probability that a. The sample mean *>$23,00 b. The sampling error is less than $800.

7. The mean price of a new car sold in Brooklyn is u =$22,500. o = $4,000. A sample of 100 new cars is chosen.. Find the probability that a. The sample mean *>$23,00 b. The sampling error is less than $800.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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